Synthetic time series data generation

Abstract

According to an example, synthetic time series data generation may include receiving time series data for a plurality of users, and applying dimensionality reduction to transform the time series data from a high dimensional space n of the time series data to a low dimensional space m, where m<n. The transformed time series data may be used to estimate a time series data density in the low dimensional space m by generating a density function. The density function may be sampled for data, and the sampled data may be transformed back to the high dimensional space n to generate the synthetic time series data.

What is claimed is: 
     
       1. A method for generating synthetic time series data from time series data collected by a time series data measurement device, the method comprising:
 receiving the time series data, wherein the time series data is stored on a memory device; 
 applying dimensionality reduction to transform the time series data from a high dimensional space n of the time series data to a low dimensional space m, wherein m<n; 
 using the transformed time series data to estimate a time series data density in the low dimensional space m by generating a density function; 
 sampling data from the density function; and 
 transforming, by a processor, the sampled data back to the high dimensional space n to generate the synthetic time series data, wherein the processor is to utilize the synthetic time series data to represent the time series data. 
 
     
     
       2. The method of  claim 1 , wherein applying dimensionality reduction to transform the time series data from the high dimensional space n of the time series data to the low dimensional space m further comprises:
 applying linear dimensionality reduction to transform the time series data from the high dimensional space n of the time series data to the low dimensional space m. 
 
     
     
       3. The method of  claim 1 , wherein applying dimensionality reduction to transform the time series data from the high dimensional space n of the time series data to the low dimensional space m further comprises:
 applying principal component analysis (PCA) to transform the time series data from the high dimensional space n of the time series data to the low dimensional space m. 
 
     
     
       4. The method of  claim 1 , wherein using the transformed time series data to estimate the time series data density in the low dimensional space m by generating the density function further comprises:
 performing a binned multivariate kernel density estimate to generate the density function. 
 
     
     
       5. The method of  claim 1 , wherein sampling data from the density function further comprises:
 randomly sampling data from the density function. 
 
     
     
       6. The method of  claim 1 , wherein transforming the sampled data back to the high dimensional space n to generate the synthetic time series data further comprises:
 projecting the sampled data back to the high dimensional space n. 
 
     
     
       7. The method of  claim 1 , wherein receiving time series data for the plurality of users further comprises:
 receiving empirical time series data for the plurality of users. 
 
     
     
       8. The method of  claim 1 , further comprising:
 determining the low dimensional space m so as to capture a predetermined amount of variance in the time series data. 
 
     
     
       9. The method of  claim 1 , wherein sampling data from the density function, and transforming the sampled data back to the high dimensional space n to generate the synthetic time series data further comprise:
 pre-sampling a plurality of data points from the density function; 
 selecting a data point from the plurality of pre-sampled data points; and 
 transforming the selected data point back to the high dimensional space n to generate the synthetic time series data. 
 
     
     
       10. The method of  claim 9 , wherein selecting the data point from the plurality of pre-sampled data points further comprises:
 randomly selecting the data point from the plurality of pre-sampled data points. 
 
     
     
       11. An apparatus to generate synthetic time series data from time series data collected by a time series data measurement device, the apparatus comprising:
 a memory storing machine readable instructions to:
 receive the time series data; 
 apply dimensionality reduction to transform the time series data from a high dimensional space n of the time series data to a low dimensional space m, wherein m<n; 
 use the transformed time series data to estimate a time series data density in the low dimensional space m by performing a binned multivariate kernel density estimate to generate a density function; 
 sample data from the density function; and 
 transform the sampled data back to the high dimensional space n to generate the synthetic time series data; and 
 
 a processor to implement the machine readable instructions, wherein the processor is to utilize the synthetic time series data to represent the time series data. 
 
     
     
       12. The synthetic time series data generation apparatus of  claim 11 , wherein to apply dimensionality reduction to transform the time series data from the high dimensional space n of the time series data to the low dimensional space m, the machine readable instructions are further to:
 apply linear dimensionality reduction to transform the time series data from the high dimensional space n of the time series data to the low dimensional space m. 
 
     
     
       13. The synthetic time series data generation apparatus of  claim 11 , wherein to sample data from the density function, the machine readable instructions are further to:
 randomly sample data from the density function. 
 
     
     
       14. The synthetic time series data generation apparatus of  claim 11 , further comprising machine readable instructions to:
 determine the low dimensional space m so as to capture a predetermined amount of variance in the time series data. 
 
     
     
       15. A non-transitory computer readable medium having stored thereon machine readable instructions to generate synthetic data from data that is collected by a time series data measurement device, the machine readable instructions, when executed, cause a computer system to:
 receive the data; 
 apply linear dimensionality reduction to transform the data from a high dimensional space n of the data to a low dimensional space m, wherein m<n; 
 use the transformed data to estimate a data density in the low dimensional space m by generating a density function; 
 sample data points from the density function; and 
 transform, by a processor, the sampled data points back to the high dimensional space n to generate the synthetic data, wherein the processor is to utilize the synthetic data to represent the data.